Ground-state phase diagram,symmetries,excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.

An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime

An analytical variational method for the ground state of the biased quantum Rabi model in the ultra-strong coupling regime is presented. This analytical variational method can be obtained by a unitary transformation or alternatively by assuming the form of the ground state wave function. The key of the method is to introduce a variational parameter λ,which can be determined by minimizing the energy functional. Using this method, we calculate the physical observables with high accuracy in comparison with the numerical exact ones. Our method evidently improves over the widely used general rotating-wave approximation（GRWA） in both qualitative and quantitative aspects.

Quantum exceptional points of non-Hermitian Hamiltonian and Liouvillian in dissipative quantum Rabi model

The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.

Hidden symmetry operators for asymmetric generalized quantum Rabi models

The hidden Z2 symmetry of the asymmetric quantum Rabi model(AQRM)has recently been revealed via a systematic construction of the underlying symmetry operator.Based on the AQRM result,we propose an ansatz for the general form of the symmetry operators for AQRM-related models.Applying this ansatz we obtain the symmetry operator for three models:the anisotropic AQRM,the asymmetric Rabi–Stark model(ARSM),and the anisotropic ARSM.

Dynamics of Rabi model under second-order Born Oppenheimer approximation

We apply the second-order Born-Oppenheimer （BO） approximation to investigate the dynamics of the Rabi model, which describes the interaction between a two-level system and a single bosonic mode beyond the rotating wave approxi- mation. By comparing with the numerical results, we find that our approach works well when the frequency of the two-level system is much smaller than that of the bosonic mode.

Unified approach to various quantum Rabi models witharbitrary parameters

A general approach is proposed to the quantum Rabi model and its several variants within the extended coherent states.The solutions to all these models including the anisotropy and the nonlinear Stark coupling are then obtained in an unified way.The essential characteristics such as the possible first-order phase transition can be detected analytically.This approach can be easily applied to the recent experiments with various tunable parameters without much additional effort,so it should be very helpful to the analysis of the experimental data.

Analytic solutions for generalized PT-symmetric Rabi models

We theoretically investigate the exact solutions for generalized parity–time(PT)-reversal-symmetric Rabi models driven by external fields with monochromatic periodic, linear, and parabolic forms, respectively. The corresponding exact solutions are presented in terms of the confluent Heun equations without any approximation. In principle, the analytic solutions derived here are valid in the whole parameter space. Such a kind of study may offer potential coherent control schemes of the PT-symmetric two-level systems.

Criticality-enhanced quantum sensing in the anisotropic quantum Rabi model

Quantum systems that undergo quantum phase transitions exhibit divergent susceptibility and can be exploited as probes to estimate physical parameters.We generalize the dynamic framework for criticality-enhanced quantum sensing by the quantum Rabi model(QRM)to its anisotropic counterpart and derive the correspondingly analytical expressions for the quantum Fisher information(QFI).We find that the contributions of the rotating-wave and counterrotating-wave interaction terms are symmetric at the limit of the infinite ratio of qubit frequency to field frequency,with the QFI reaching a maximum for the isotropic QRM.At finite frequency scaling,we analytically derive the inverted variance of higher-order correction and find that it is more affected by the rotating-wave coupling than by the counterrotating-wave coupling.

Multiphonon-resonance quantum Rabi model and adiabatic passage in a cavity-optomechanical system

In this paper,we propose a scheme to achieve a multiphonon-resonance quantum Rabi model and adiabatic passage in a strong-coupling cavity optomechanical system.In the scheme,when the driving bichromatic laser beam is adjusted to the off-resonant j-order red-and blue-sideband,the interaction between the cavity and mechanical oscillator leads to a j-phonon resonance quantum Rabi model.Moreover,we show that there exists a resonant multi-phonon coupling via intermediate states connected by counter-rotating processes when the frequency of the simulated bosonic mode is near a fraction of the transition frequency of the simulated two-level system.As a typical example,we theoretically analyze the two-phonon resonance quantum Rabi model,and derive an effective Hamiltonian of the six-phonon coupling.Finally,we present a method of six-phonon generation based on adiabatic passage across the resonance.Numerical simulations confirm the validity of the proposed scheme.Theoretically,the proposed scheme can be extended to the realization of 3j-phonon state.

Exact solution of the two-mode quantum Rabi model

An analytical method is developed to study the two-mode quantum Rabi model.For certain specific parameter conditions,especially for the resonant conditions,we obtain an infinite number of the exact solutions of the eigenfunctions and associated energies.It is shown that there exist new types of the exact energies which do not correspond to the level-crossings.Our analytical method may find applications in some related models.

Parity Symmetry and Parity Breaking in the Quantum Rabi Model with Addition of Ising Interaction

We explore the possibility to generate new parity symmetry in the quantum Rabi model after a bias is introduced. In contrast to a mathematical treatment in a previous publication [J. Phys. A 46(2013) 265302], we consider a physically realistic method by involving an additional spin into the quantum Rabi model to couple with the original spin by an Ising interaction, and then the parity symmetry is broken as well as the scaling behavior of the ground state by introducing a bias. The rule can be found that the parity symmetry is broken by introducing a bias and then restored by adding new degrees of freedom. Experimental feasibility of realizing the models under discussion is investigated.

Spatiotemporal Analysis and Predictive Modeling of Rabies in Tennessee

Among viruses, Rhabdovirus, more commonly known as rabies, is largely monitored throughout landscapes because of its known risks and deadliness. While vaccination and education efforts have been enforced and apparently successful in the past decades, many questions still exist in some regions about the virus’s spread and potential. In the United States, the state of Tennessee’s Department of Health has documented rabies reports from the 1940s-2010s, but not as many spatial analyses have been performed to further map and assess rabid animals in this variable landscape. Our study proposed to create distribution and density models to give an idea of the types of locations rabid animals have consistently been found. A predictive model was also created using software that simulated landscape fragmentation and habitat connectivity, to provide further insight for potential disease spread. Our results display that Tennessee’s central region, which is a more homogenous landscape, tended to host a lot of rabid animals and maintained a rather consistent distribution throughout the years. The predictive model was simulated on a less homogenous landscape and displayed that spread potential can be affected by natural barriers. Each of these spatial results could be of service in future disease monitoring, hopefully for the benefit of wildlife and people alike.

基于两量子比特Rabi模型暗态解的Bell态制备

Bell态在量子光学和量子信息中具有重要的应用价值.该文基于两量子比特Rabi模型的特殊暗态制备单光子源的方案,重点探究了Bell态的同时确定性制备,并研究了有无单光子释放的情况下,环境对制备Bell态保真度的影响.数值结果表明,所提出的方案可以制备确定性的Bell态,并且在耗散环境下能保持高保真度.

量子力学表示理论的一种实现

量子力学创立伊始,狄拉克就关注到了一般表示的问题,其后量子力学的发展又引入了福克态、相干态等表示。好的表示应能提供正交归一的完备基,同时又能给出问题的严格解析解或者允许方便地得到近似解,但这常常是做不到的。我们意识到此前得到的相干态正交化方法恰恰满足表示理论的一般性要求,且因为包含自由参数为构造归一化的完备正交基实际上提供了无限的选择,这样甚至在解决问题的过程中都可以灵活地选择不同的表示,从而带来计算量的大幅减小。通过对不同耦合强度下的近共振态Rabi模型最初10个能级的计算,并同关联的JC模型的结果相比较,验证了相干态正交化方法的有效性。

量子Rabi模型中的Berry相的解析解

利用光子Fock态,给出量子Rabi模型的数值严格解,其结果比推广的转动波近似有很大改进.截取两个Fock态,可以给出简单明了的解析结果,在很大的耦合区间里,非常接近严格解,包含了主要的非旋波效应.我们获得Berr相的简明解析结果,与数值严格解在很大区间内吻合.

中国2004—2019年狂犬病时空分布特征与气象因素驱动效应研究

目的了解我国2004—2019年狂犬病的疾病负担现状及其分布特点,深入分析我国国家监测点狂犬病病例的时空分布规律,探究气象因素对狂犬病发病的驱动效应,旨在为防疫策略的制定提供科学支撑。方法收集中国2004—2019年我国狂犬病的时间、地区及人群等病例数据及同期月度气象数据,描述疾病负担现状及流行特征;使用SaTScan 9.0进行时空季节扫描,探究全国各省份聚集效应。通过拟合Quasi-Poisson分布滞后非线性模型,研究月平均相对湿度、月平均相对温度、月累积降水量、日照时长对狂犬病发病的驱动效应。结果2004—2019年中国报告狂犬病共计26605例,广西壮族自治区发病数居全国首位,关于狂犬病疾病负担的年估计百分变化比皆处于下降趋势;季节性高峰集中在6~11月份,对数似然比为516.14;我国狂犬病发病多集中于南部地区,并且有向中部地区扩大蔓延;狂犬病发病在时间尺度上受相对湿度、气温、降水量和日照时长的影响显著,其月平均相对湿度为74.75%、平均气温为8.725℃、平均降水量为59.25 mm、月累计日照时长56.575 h。月平均温度对狂犬病发病率的相对危险度在滞后3个月时达到高峰,相对风险为4.48,月总计日照总时长与狂犬病发病率相对危险度在滞后2个月时达到高峰,相对风险为1.21。结论全国狂犬病全年均有发病且夏秋季高发。狂犬病疾病负担呈下降趋势,但狂犬病病例依旧存在疾病风险,且发病地区较为集中,有较明确的地域性特点,主要分布于中国中部以及南部等地。气温、日照时长等气象因素对疾病发生具有显著驱动作用。

Rabi模型的分析与计算

Rabi模型是量子光学的基础模型之一,它描述了一个二能级原子系统与腔内光场的相互作用.但尽管Rabi模型在物理学中有重要地位,它并不能被精确解析求解.通常的办法是将Rabi模型在旋波近似下转化为JC模型,则可以解析求解,然而JC模型只能描述量子光腔的强耦合作用,不能描述超强耦合作用.在这个工作中,为了求解Rabi模型,我们采用Phy.Rev.A,2012,86(1):2271一文中的方法对其哈密顿量进行U=exp[λσx(a++a)]的幺正变换,忽略a+和a的高阶项,将其投影在σz的本征态上,其中σz|±z〉=±|±z〉,得到一个类JC模型,再对所得哈密顿量进行分析,可以得出能量谱和波函数.在MATLAB中进行数值模拟,将数值模拟的结果与解析结果进行对比,我们发现在低能级区物理图像吻合良好.

Jaynes-Cummings晶格模型和Rabi晶格模型的量子相变

采用平均场近似的方法,分别研究了Jaynes-Cummings晶格模型和Rabi晶格模型的量子相变:Mott绝缘体相-超流体相量子相变,探索了光的聚束-反聚束行为,研究了Kerr非线性作用对量子相变与光子统计特征的影响.研究结果表明,在Rabi晶格模型中二能级原子和光子相互作用强度g和格点之间光子跃迁强度J的增大会使晶格体系从Mott绝缘体相向超流体相转变,同时,光子统计行为由聚束转变为反聚束,而Kerr非线性强度的增大抑制了Mott绝缘体相-超流体相相变,但促进了光子聚束与反聚束之间的转变.

囚禁离子非线性Rabi模型量子场熵演化特性

本文研究了基于单个囚禁离子与两束激光场相互作用的非线性Rabi模型中的纠缠动力学.利用Von-Neumann熵来表征纠缠度.通过数值模拟,详细讨论了Lamb-Dicke参数对量子场熵的影响.在单光子非线性Rabi模型中,随着Lamb-Dicke参数和初始平均光子数的增加,场熵的平均值并不单调增加.在双光子非线性Rabi模型中,场熵的时间演化是周期性振荡的.随着Lamb-Dicke参数的增加,场熵的周期振荡逐渐消失.对于较小的Lamb-Dicke参数,纠缠和退纠缠周期性地出现.

有偏置的Rabi模型的能谱与Berry相

利用Fock态展开的方法对Rabi模型和有偏置的Rabi模型严格求解,得到相对应的本征能谱和Berry相,为了方便计算,对Rabi模型进行了旋转变换,从而更加直观地反映系统的宇称对称性。用MATLAB进行数值模拟,得到了有无偏置的Rabi模型的能量本征值和Berry相随耦合强度而变化的图像,并将所得结果进行对比分析。研究发现:由于偏置项的存在打破了系统的奇偶对称性,使宇称不再守恒,对系统的能谱和Berry相都产生了较大影响,特别是在共振情况下有无偏置项的Rabi模型的Berry相有很大的不同,这对量子比特调控具有指导意义。